Abstract

\section{Motivation:}
Many problems in data integration in bioinformatics can be posed as one
common question: Are two sets of observations generated by the same
distribution? We propose a kernel-based statistical test for this problem, based on the fact that two
distributions are different if and only if there exists at least one
function having different expectation on the two distributions.
Consequently we use the maximum discrepancy between function means as the
basis of a test statistic.
The Maximum Mean Discrepancy (MMD) can take advantage of the kernel
trick, which allows us to apply it not only to vectors, but strings,
sequences, graphs, and other common structured data types arising in
molecular biology.
\section{Results:}
We study the practical feasibility of an MMD-based test on three central
data integration tasks: Testing cross-platform comparability of
microarray data, cancer diagnosis, and data-content based schema
matching for two different protein function classification schemas. In
all of these experiments, including high-dimensional ones, MMD is very accurate in finding samples that
were generated from the same distribution, and outperforms its best competitors.
\section{Conclusions:}
We have defined a novel statistical test of whether two samples are from the same distribution,
compatible with both multivariate and structured data, that is fast, easy to implement, and
works well, as confirmed by our experiments.